頂ちょう戴だいN3
ください is the standard polite way to request something, while ちょうだい is a softer, more casual (often feminine or child-directed) way to say the same thing among family or close friends.
どうぞN5
ください is the direct request form attached to a verb ('please give/do'), while どうぞ is the standalone softener that often accompanies it.
お願ねがいしますN4
ください is a polite imperative for direct requests, while お願いします is a humble expression that softens the request and shows deference.

Etymology

Irregular imperative form of the honorific verb くださる (to give). The form ください became fixed as a polite request auxiliary.

給たまうN1

ください is the modern, standard way to make a polite request; the suffix 給う (as in its imperative form 給え) serves the same function but sounds archaic and literary.

なさい

ください is a polite request form usable with anyone, while なさい is a plainer command typically used by a superior toward an inferior, such as a parent to a child.

Politeness

頂ちょう戴だいplainN3
ください is the polite way to ask for something, while ちょうだい is a casual, often feminine or child-like version of the same request.

Don't confuse with

下くださるN4
くださる is the plain honorific verb meaning 'to give (to me)', while ください is its special imperative form used to make a polite request, so learners must remember to switch to ください (not くださる) when actually asking for something.
お願ねがいいたします
ください directly attaches to a verb to mean 'please do ~', while お願いいたします is a standalone humble formula often used with nouns, as in ご確認をお願いいたします.